@prospect1: Many schools that claim to be need-blind are, but do not or can not meet full-need. Key difference.
And yes, there must be a healthy proportion of full-pay students at all colleges (besides Harvard and maybe YPSM and the WASP LACs, who have a stupendous amount of endowment per student), but the percentage of the pool of students who are competitive for the Ivies/equivalents (with the near-perfect test score, near-perfect GPA, and amazing ECs) who are no-need is not a tiny percentage. The composition of the pool of students who are competitive for the Ivies/equivalents is far different from the composition of the US HS population as a whole.
Depending on where you grow up, you may not realize this, but there are a lot of upper-middle-class and rich families who’s kids are competitive for the Ivies/equivalents.
Just consider this: Few kids would turn down a private Ivy/equivalent for UC-Berkeley or UMich, yet the admission standards of those schools for OOS applicants are now close to that of the lower Ivies (or at least Cornell), the number of OOS students each of them take in is equal to the entire undergraduate population of a bigger Ivy, and the vast majority of the OOS students attending those publics do not get any meaningful FA from those schools.
So just below the Ivy-level are 2 whole Ivies’ worth of no-need students (not to mention the no-need students going to ND, Georgetown, and Tufts). Is it so hard to imagine that there are a ton of impressive no-need applicants at the Ivy/equivalent-level as well?
Plus, note that the vast majority of international students at most American universities are full-pay.